Friction induced hunting limit cycles: A comparison between the LuGre and switch friction model

In this paper, friction induced limit cycles are predicted for a simple motion system consisting of a motor-driven inertia subjected to friction and a PID-controlled regulator task. The two friction models used, i.e., (i) the dynamic LuGre friction model and (ii) the static switch friction model, are compared with respect to the so-called hunting phenomenon. Analysis tools originating from the field of nonlinear dynamics will be used to investigate the friction induced limit cycles. For a varying controller gain, stable and unstable periodic solutions are computed numerically which, together with the stability analysis of the closed-loop equilibrium points, result in a bifurcation diagram. Bifurcation analysis for both friction models indicates the disappearance of the hunting behavior for controller gains larger than the gain corresponding to the cyclic fold bifurcation point.

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